Re: Factor Rings

note that the elements of Z3[x]/<x2 - 1> will be cosets that we can represent as polynomials of degree < 2, to save on notation instead of writing p(x) + I, i will simply write p(u), and thus u = x + I, and i will write a instead of a + I

Re: Factor Rings

i think this is a great example of how the additive structure of a ring can have very little to do with the multiplicative structure. and that different multiplicative structures on the very same abelian group can produce VERY different results. put another way: the cardinality of a finite ring tells us a lot less than we might hope.